@inproceedings{c0541515dcd24605bded28b350114b87,
title = "The Parametrized Complexity of the Segment Number",
abstract = "Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph G, the segment number of G is the minimum number of segments that can be achieved by any planar straight-line drawing of G. The line cover number of G is the minimum number of lines that support all the edges of a planar straight-line drawing of G. Computing the segment number or the line cover number of a planar graph is ∃ R -complete and, thus, NP-hard. We study the problem of computing the segment number from the perspective of parameterized complexity. We show that this problem is fixed-parameter tractable with respect to each of the following parameters: the vertex cover number, the segment number, and the line cover number. We also consider colored versions of the segment and the line cover number.",
keywords = "Line cover number, Parameterized complexity, Segment number, Vertex cover number, Visual complexity",
author = "Sabine Cornelsen and {Da Lozzo}, Giordano and Luca Grilli and Siddharth Gupta and Jan Kratochv{\'i}l and Alexander Wolff",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 31st International Symposium on Graph Drawing and Network Visualization, GD 2023 ; Conference date: 20-09-2023 Through 22-09-2023",
year = "2023",
month = jan,
day = "1",
doi = "10.1007/978-3-031-49275-4_7",
language = "English",
isbn = "9783031492747",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "97--113",
editor = "Bekos, {Michael A.} and Markus Chimani",
booktitle = "Graph Drawing and Network Visualization - 31st International Symposium, GD 2023, Revised Selected Papers",
address = "Germany",
}